Primer on Acoustic Guitars and Sound - Vintage Gypsy Guitars - Busato- Favino-Di Mauro-Castelluccia

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Primer on Acoustic Guitars and Sound

Technical Info

Primer on acoustic guitars and sound:

All acoustic guitars share similar anatomy. The strings are fastened to a guitar at the bridge and the peg head, and vibrate between the nut at the end of the neck and the saddle on the bridge. The twelfth fret is located at exactly the middle of the strings. The tuners allow the tension of the strings to be changed, and the bridge transfers the vibrations to the soundboard. When a note is played, the strings vibrate both the top of the guitar as well as the air inside the body of the guitar. These vibrations on the top and in the body of the guitar produce sound.
In order to understand how a guitar works, one must first understand how sound behaves. Sound travels in the form of a wave. There are two types of sound waves, longitudinal and transverse. Longitudinal waves travel parallel to the source of the wave and transverse waves travel perpendicular to the source of the wave. Sound is produced from vibrations through a medium, and travels in the form of longitudinal waves. The frequency at which the vibrations occur is referred to as the pitch. In music, pitch relates to the note being played.
The vibrations caused from a disturbance such as a vibrating string create areas of compression and rarefaction of the molecules in the medium that the vibrations are traveling through. Sound is only produced when these vibrations are traveling through a medium. An observer is able to hear sounds because these areas of compression and rarefaction are picked up by the observer’s ears, and translated to the brain.
The volume of a sound depends on the amount of air that is moving due to the vibrations created from the sound source. When an object that is vibrating is held against another object, the second object will also vibrate. This is called forced vibration. If the second object has a larger surface area, the vibrations will move more air, making the volume louder. One of the main physics principles that apply to an acoustic guitar is forced vibrations. Forced vibrations occur when a vibrating object forces another object to vibrate. Hewitt uses the example of a tuning fork placed on a table. The vibrating tuning fork forces the table to vibrate at the same frequency. The vibrating table moves more air molecules than the tuning fork alone, and therefore produces a higher volume. On a guitar, the vibration of the strings is transferred to the soundboard through the bridge, forcing the soundboard to vibrate at the same frequency as the string, which produces sound.
There are three different kinds of guitars: classical, folk and gypsy jazz. The main visible difference between a classical and a folk guitar or a gypsy jazz guitar is the type of strings used. Classical guitars use nylon strings and folk and gypsy jazz guitars use steel strings. All types of guitars are tuned to the same frequencies, but the nylon strings have a much lower density than steel strings, and therefore the tension on the soundboard of the guitar is much less for a classical guitar than a folk guitar or a gypsy jazz guitar. The bracing for a steel string guitar must be much stronger than the bracing of a classical guitar in order to handle the increased force on the soundboard due to the steel strings.  
When a note is played on the guitar, the string vibrates back and fourth producing a wave. The frequency of the note is determined by the velocity of the wave on the string divided by the wavelength.
A guitar has six strings, each one of a different thickness and tuned to a different frequency. The strings must be different thicknesses because the velocity of a wave on a string depends on the tension. The thicker strings have a lower frequency, and the thinner strings have a higher frequency. This is because thicker strings have a higher linear mass density, which reduces the velocity of the wave on the string for a given tension, and the result is a lower frequency. Regardless of whether or not a guitar is strung with nylon or steel strings, the frequency of the open strings, or the frequency produced when a string is not fretted, is not changed. Depending on the size of the instrument (and therefore the wavelength of the string), the velocity will change. For a given frequency, a long wavelength means a lower velocity, and a short wavelength means a higher velocity. The strings on all guitars in standard tuning are tuned to the same frequencies, despite the length of the strings. Small guitars are tuned to the same frequencies as larger guitars.

String Pitch Frequency
1 E2 82 Hz
2 A2 110 Hz
3 D3 147 Hz
4 G3 196 Hz
5 B3 243 Hz
6 E4 330 Hz

The tension on the bridge of the guitar due to the strings varies depending on the material of the strings due to the change in the linear mass density. Table 2 compares the tension of the most common gauge of nylon and steel strings. The tensions shown in Table 2 are based on the most common scale length of each style of guitar; 25.6 for nylon, 25.4 for steel.

String Nylon (Normal Tension)  Steel (Light Gauge)
1st E 14 Lbs 25.1 Lbs
2nd A 15 Lbs 28.4 Lbs
3rd D 15.6 Lbs 29.5 Lbs
4th G 12.1 Lbs 29.4 Lbs
5th B 11.6 Lbs 23.3 Lbs
6th E 15.3 Lbs 23.3 Lbs
Total 83.6 Lbs 159 Lbs

In order to change the note being played, the player changes the wavelength of the string by shortening the length of the string with their fingers. The velocity of the wave on the string remains constant, and by shortening the length of the string the frequency increases.
The wavelength for a string on a guitar depends on the scale length of a guitar, or the distance from the nut near the headstock of the guitar to the saddle on the bridge, with the twelfth fret being in the middle. The first harmonic, or the fundamental, shows the motion of a plucked open string (vibrating between the nut and the saddle), which is half the wavelength of the wave on the string. This is known as the first harmonic. Harmonics are whole number multiples of the fundamental frequency. The second harmonic is formed on a guitar by creating a node at the twelfth fret and is twice the frequency of the open string. Creating a node at the fifth or seventeenth fret forms the third harmonic and the frequency is three times higher than the open string. There are two different phenomena that make the conversion of the mechanical energy from the player plucking a string to sound energy more efficient, and therefore louder. Physics experts note that a guitar does not amplify the sound from the vibrations of the strings. First, when the string vibrates above the sound hole of the guitar, the vibrations of the strings create areas of compressions and rarefaction in the air around the sound hole. These vibrations compress the air inside the body of the guitar, which raises the internal pressure. The air is then forced out due to the high pressure. This is referred to as Helmholtz resonance. The vibration of the air inside the body of a guitar mostly affects the lower frequencies, so a guitar with a smaller body would produce softer low frequencies. This becomes apparent when looking at the violin family of instruments. The lower pitched instruments such as the cello or bass have larger bodies than the violin of viola.
The other way that a guitar converts the mechanical energy to sound energy is through the vibration of the top of the guitar. The top or soundboard is designed to vibrate, and because of its large surface area, the vibrations move more air than the string alone could. The vibrating soundboard is an example of forced vibrations. The strings vibrate against the bridge, which forces the soundboard to vibrate. The soundboard projects the higher frequencies of a guitar into the air around the guitar. The more surface area of the soundboard, the louder the produced frequencies are. The combination of the low frequencies projected from the vibration of the air inside the body of the guitar as well as the high frequencies projected from the vibration of the soundboard gives the guitar its unique sound.
Every instrument’s sound quality or timbre is different due to the instrument’s unique overtone series. When a note is played on a guitar, the pitch that is heard is the fundamental frequency. There is also a combination of other frequencies, known as partial tones or harmonics, which are emitted along with the fundamental frequency. The volumes of these partial tones affect the timbre or tone of the instrument. The amount of partial tones and the volume of each partial tone for a note make every instrument sound different. The combination of these partial tones is known as the overtone series. The overtone series is unique for not only every instrument, but also every guitar. There are several components that affect the overtone series of a guitar, from the woods used for the instrument to how the strings are plucked. Arguably the leading factor that affects the overtone series of a guitar is the bracing on the underside of the soundboard.
The purpose of the bracing of a guitar is to both provide support against the soundboard warping due to the tension of the strings as well as help transfer the vibrations of the strings to the soundboard. Ideally, the bracing transfers the vibration of the strings to the entire soundboard of the instrument.
In about 1850 Antonio Torres of Spain introduced a fanned bracing pattern on his nylon string guitars. His bracing pattern provided sufficient strength to the soundboard of the guitar as well as enhanced the tone of the instrument. This pattern has remained one of the most common bracing techniques used for classical guitars to this day. Steel guitar strings began to become available by the early 20th century and proved to provide louder volumes than nylon strings. While Torres’ pattern was sufficient for nylon strings, the increased tension of the steel strings was too high and caused the soundboard to warp. To compensate for this, guitar builders began using different bracing pattern, which provided more support for the soundboard. Christian Martin who founded C.F. Martin guitars in the 1830’s was an innovator of the X bracing pattern. Martin’s X bracing pattern has remained the standard for steel string guitar bracing while Torres’ fan bracing pattern has remained the standard for nylon string guitars. And ladder bracing created by Luigi Mozzani remained the standard for all gypsy jazz guitars, from Selmer to Busato, Di Mauro, Castelluccia, Favino, etc.
The soundboard of a guitar is designed to oscillate due to the vibrations of the strings. The more that the soundboard is able to flex, the more volume the instrument produces because of the higher amount of air being vibrated. A soundboard with no bracing would be much louder than a soundboard with bracing because the soundboard would be free to vibrate, but the tension of the strings would cause the wood to warp, making the instrument unplayable. Guitar builders explain that the structural requirements of a guitar harm the musical quality of the instrument. The soundboard of a guitar oscillates in different patterns depending on the frequency of the note being played. One way to visualize these patterns is with Chladni figures. Chladni figures provide a visual reference for where the nodes are located. When the soundboard is vibrating at a certain frequency, there are areas that on the soundboard that do not vibrate due to standing waves, or stationary waves. Standing waves occur when two opposing waves of the same wavelength and amplitude meet and cancel. When a material such as sand or some kind of power is placed on a plate (or soundboard) that is vibrating at a certain frequency, it is attracted to the areas that are not moving, or nodes.
The nodes are formed on a guitar soundboard when waves encounter each other and cancel. Even if one note is plucked on a guitar string, the interference of the vibrations on the soundboard still form nodes. Waves on the soundboard of a guitar travel in two dimensions. Chladni figures can be helpful in guitar construction. Guitar builders can use the patterns to determine how the bracing on the soundboard needs to be altered. Altering the bracing on the soundboard until a desired chladni pattern is found is referred to as free plate tuning.
While the patterns formed on the soundboard depend on the shape and material of the soundboard, the patterns can be useful for the final shaping of the braces. While the main purpose of the braces is to provide structural support for the soundboard, they also help transmit the vibration of the strings to the entire soundboard. The braces must be shaped in such a way that the stiffness to mass ratio of the soundboard is the same in all directions.
One method of ensuring that the stiffness to mass ratio is consistent along the soundboard is by using the ring-and-a-half method. In order to use this method, the soundboard is vibrated at different frequencies until a Chladni figure forms where the nodes form a ring below the sound hole, and half a ring above the sound hole. The frequency at which this pattern occurs varies depending on the soundboard being tested.
Once the frequency that forms the ring-and-a-half pattern is found, the braces on the soundboard can be shaped to improve the pattern. The goal is to have a perfect circle below the sound hole where the bridge is attached as well as a perfectly curved line above the sound hole. By changing the height and width of the braces, the resistance against flexing is changed. A thinner brace will flex more than a thick brace. There is a precise equation (R=1/12 x (w) x (h cube), which shows the relationship of how height and width of a brace affects the resistance against bowing, where R is the resistance, (w) is the width of the brace and (h) is the height of the brace.
When constructing the soundboard for a guitar, the braces are shaved down, reducing the resistance against flex, until the ring-and-a-half pattern is perfect. When the ring-and-a-half pattern is perfect, the stiffness to mass ratio of the soundboard is isotropic, or consistent across the entire soundboard. The thickness of the bracing also has effect on the tone or timbre of a guitar. Guitars with heavy bracing have better tone, but less volume. This is due to the fact that the heavy bracing doesn’t allow the soundboard to vibrate as well, therefore moving less air. Lighter bracing does not transmit the vibration of the strings to the soundboard as efficiently as thick bracing, but it allows the soundboard to vibrate more because it is less stiff, producing more volume.
While the X bracing pattern for steel string guitars and the fan-bracing pattern for nylon string guitars have been the most commonly practiced bracing techniques, some guitar builders have experimented with alternative bracing patterns, and the gypsy guitar makers made their own bracing patterns.
There are many elements that go into producing a quality guitar. Both classical and folk guitar builders strive to produce instruments with good tone as well as powerful volume. While there is a lot to be said about the materials used in constructing a guitar, one can argue that the bracing is one of the most important aspects. Guitar builders, also known as luthiers, are constantly making adjustments to the standard X bracing and fan-bracing patterns in order to create an instrument that creates ideal conditions for sound to travel. Gypsy guitar makers always used ladder bracing. The design of a guitar is based on several physics concepts that can be utilized to produce an instrument of the highest quality.

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